tomaarsen/csr-mxbai-embed-large-v1-nq

Sparse CSR model trained on Natural Questions

This is a CSR Sparse Encoder model finetuned from mixedbread-ai/mxbai-embed-large-v1 on the natural-questions dataset using the sentence-transformers library. It maps sentences & paragraphs to a 4096-dimensional sparse vector space and can be used for semantic search and sparse retrieval.

Model Details

Model Description

• Model Type: CSR Sparse Encoder
• Base model: mixedbread-ai/mxbai-embed-large-v1
• Maximum Sequence Length: 512 tokens
• Output Dimensionality: 4096 dimensions
• Similarity Function: Dot Product
• Training Dataset:
  • natural-questions
• Language: en
• License: apache-2.0

Model Sources

• Documentation: Sentence Transformers Documentation
• Documentation: Sparse Encoder Documentation
• Repository: Sentence Transformers on GitHub
• Hugging Face: Sparse Encoders on Hugging Face

Full Model Architecture

SparseEncoder(
  (0): Transformer({'max_seq_length': 512, 'do_lower_case': False}) with Transformer model: BertModel 
  (1): Pooling({'word_embedding_dimension': 1024, 'pooling_mode_cls_token': True, 'pooling_mode_mean_tokens': False, 'pooling_mode_max_tokens': False, 'pooling_mode_mean_sqrt_len_tokens': False, 'pooling_mode_weightedmean_tokens': False, 'pooling_mode_lasttoken': False, 'include_prompt': True})
  (2): CSRSparsity({'input_dim': 1024, 'hidden_dim': 4096, 'k': 256, 'k_aux': 512, 'normalize': False, 'dead_threshold': 30})
)

Usage

Direct Usage (Sentence Transformers)

First install the Sentence Transformers library:

pip install -U sentence-transformers

Then you can load this model and run inference.

from sentence_transformers import SparseEncoder

# Download from the 🤗 Hub
model = SparseEncoder("tomaarsen/csr-mxbai-embed-large-v1-nq")
# Run inference
sentences = [
    'who is cornelius in the book of acts',
    'Cornelius the Centurion Cornelius (Greek: Κορνήλιος) was a Roman centurion who is considered by Christians to be one of the first Gentiles to convert to the faith, as related in Acts of the Apostles.',
    "Joe Ranft Ranft reunited with Lasseter when he was hired by Pixar in 1991 as their head of story.[1] There he worked on all of their films produced up to 2006; this included Toy Story (for which he received an Academy Award nomination) and A Bug's Life, as the co-story writer and others as story supervisor. His final film was Cars. He also voiced characters in many of the films, including Heimlich the caterpillar in A Bug's Life, Wheezy the penguin in Toy Story 2, and Jacques the shrimp in Finding Nemo.[1]",
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# (3, 4096)

# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [3, 3]

Evaluation

Metrics

Sparse Information Retrieval

• Datasets: NanoMSMARCO_128, NanoNFCorpus_128 and NanoNQ_128
• Evaluated with SparseInformationRetrievalEvaluator with these parameters:

  {
      "max_active_dims": 128
  }
  

Metric	NanoMSMARCO_128	NanoNFCorpus_128	NanoNQ_128
dot_accuracy@1	0.36	0.3	0.44
dot_accuracy@3	0.6	0.58	0.58
dot_accuracy@5	0.66	0.64	0.66
dot_accuracy@10	0.78	0.66	0.76
dot_precision@1	0.36	0.3	0.44
dot_precision@3	0.2	0.32	0.1933
dot_precision@5	0.132	0.284	0.132
dot_precision@10	0.078	0.224	0.082
dot_recall@1	0.36	0.0206	0.43
dot_recall@3	0.6	0.0764	0.54
dot_recall@5	0.66	0.0909	0.6
dot_recall@10	0.78	0.1095	0.73
dot_ndcg@10	0.5701	0.2706	0.576
dot_mrr@10	0.5032	0.4388	0.5402
dot_map@100	0.5145	0.1157	0.5349
row_non_zero_mean_query	128.0	128.0	128.0
row_sparsity_mean_query	0.9688	0.9688	0.9688
row_non_zero_mean_corpus	128.0	128.0	128.0
row_sparsity_mean_corpus	0.9688	0.9688	0.9688

Sparse Nano BEIR

• Dataset: NanoBEIR_mean_128
• Evaluated with SparseNanoBEIREvaluator with these parameters:

  {
      "dataset_names": [
          "msmarco",
          "nfcorpus",
          "nq"
      ],
      "max_active_dims": 128
  }
  

Metric	Value
dot_accuracy@1	0.3667
dot_accuracy@3	0.5867
dot_accuracy@5	0.6533
dot_accuracy@10	0.7333
dot_precision@1	0.3667
dot_precision@3	0.2378
dot_precision@5	0.1827
dot_precision@10	0.128
dot_recall@1	0.2702
dot_recall@3	0.4055
dot_recall@5	0.4503
dot_recall@10	0.5398
dot_ndcg@10	0.4722
dot_mrr@10	0.4941
dot_map@100	0.3884
row_non_zero_mean_query	128.0
row_sparsity_mean_query	0.9688
row_non_zero_mean_corpus	128.0
row_sparsity_mean_corpus	0.9688

Sparse Information Retrieval

• Datasets: NanoMSMARCO_256, NanoNFCorpus_256 and NanoNQ_256
• Evaluated with SparseInformationRetrievalEvaluator with these parameters:

  {
      "max_active_dims": 256
  }
  

Metric	NanoMSMARCO_256	NanoNFCorpus_256	NanoNQ_256
dot_accuracy@1	0.36	0.4	0.44
dot_accuracy@3	0.64	0.56	0.7
dot_accuracy@5	0.76	0.64	0.76
dot_accuracy@10	0.84	0.76	0.82
dot_precision@1	0.36	0.4	0.44
dot_precision@3	0.2133	0.3467	0.2333
dot_precision@5	0.152	0.316	0.156
dot_precision@10	0.084	0.27	0.088
dot_recall@1	0.36	0.0239	0.42
dot_recall@3	0.64	0.0606	0.66
dot_recall@5	0.76	0.0838	0.71
dot_recall@10	0.84	0.1457	0.79
dot_ndcg@10	0.602	0.3186	0.6113
dot_mrr@10	0.5252	0.5102	0.5685
dot_map@100	0.5322	0.1354	0.5538
row_non_zero_mean_query	256.0	256.0	256.0
row_sparsity_mean_query	0.9375	0.9375	0.9375
row_non_zero_mean_corpus	256.0	256.0	256.0
row_sparsity_mean_corpus	0.9375	0.9375	0.9375

Sparse Nano BEIR

• Dataset: NanoBEIR_mean_256
• Evaluated with SparseNanoBEIREvaluator with these parameters:

  {
      "dataset_names": [
          "msmarco",
          "nfcorpus",
          "nq"
      ],
      "max_active_dims": 256
  }
  

Metric	Value
dot_accuracy@1	0.4
dot_accuracy@3	0.6333
dot_accuracy@5	0.72
dot_accuracy@10	0.8067
dot_precision@1	0.4
dot_precision@3	0.2644
dot_precision@5	0.208
dot_precision@10	0.1473
dot_recall@1	0.268
dot_recall@3	0.4535
dot_recall@5	0.5179
dot_recall@10	0.5919
dot_ndcg@10	0.5107
dot_mrr@10	0.5346
dot_map@100	0.4071
row_non_zero_mean_query	256.0
row_sparsity_mean_query	0.9375
row_non_zero_mean_corpus	256.0
row_sparsity_mean_corpus	0.9375

Sparse Information Retrieval

• Datasets: NanoClimateFEVER, NanoDBPedia, NanoFEVER, NanoFiQA2018, NanoHotpotQA, NanoMSMARCO, NanoNFCorpus, NanoNQ, NanoQuoraRetrieval, NanoSCIDOCS, NanoArguAna, NanoSciFact and NanoTouche2020
• Evaluated with SparseInformationRetrievalEvaluator

Metric	NanoClimateFEVER	NanoDBPedia	NanoFEVER	NanoFiQA2018	NanoHotpotQA	NanoMSMARCO	NanoNFCorpus	NanoNQ	NanoQuoraRetrieval	NanoSCIDOCS	NanoArguAna	NanoSciFact	NanoTouche2020
dot_accuracy@1	0.32	0.66	0.78	0.4	0.78	0.38	0.4	0.52	0.9	0.44	0.32	0.64	0.5714
dot_accuracy@3	0.44	0.88	0.9	0.58	0.9	0.7	0.58	0.72	0.98	0.68	0.8	0.72	0.8367
dot_accuracy@5	0.52	0.94	0.94	0.62	0.94	0.74	0.64	0.76	0.98	0.78	0.86	0.8	0.898
dot_accuracy@10	0.66	0.94	0.96	0.76	1.0	0.82	0.72	0.8	1.0	0.84	0.94	0.84	1.0
dot_precision@1	0.32	0.66	0.78	0.4	0.78	0.38	0.4	0.52	0.9	0.44	0.32	0.64	0.5714
dot_precision@3	0.16	0.6467	0.3067	0.28	0.5	0.2333	0.36	0.24	0.4	0.3467	0.2667	0.2467	0.5374
dot_precision@5	0.128	0.604	0.196	0.2	0.336	0.148	0.32	0.152	0.26	0.288	0.172	0.172	0.5306
dot_precision@10	0.1	0.49	0.1	0.124	0.176	0.082	0.258	0.086	0.14	0.208	0.094	0.094	0.4306
dot_recall@1	0.16	0.0691	0.7267	0.1779	0.39	0.38	0.0422	0.51	0.7907	0.0947	0.32	0.615	0.0388
dot_recall@3	0.205	0.1784	0.8567	0.3991	0.75	0.7	0.0783	0.67	0.9353	0.2157	0.8	0.69	0.1098
dot_recall@5	0.255	0.2625	0.9067	0.4547	0.84	0.74	0.0953	0.7	0.966	0.2977	0.86	0.775	0.1862
dot_recall@10	0.3833	0.3507	0.9267	0.5628	0.88	0.82	0.1247	0.77	1.0	0.4267	0.94	0.83	0.2847
dot_ndcg@10	0.3182	0.6035	0.8475	0.4422	0.8076	0.6106	0.3188	0.6459	0.9508	0.4004	0.6565	0.7238	0.4824
dot_mrr@10	0.4123	0.7787	0.849	0.5031	0.851	0.5419	0.4988	0.6175	0.9395	0.5814	0.5626	0.6969	0.727
dot_map@100	0.2534	0.4434	0.8125	0.3727	0.7533	0.551	0.1473	0.6086	0.9286	0.3236	0.5651	0.6904	0.3484
row_non_zero_mean_query	256.0	256.0	256.0	256.0	256.0	256.0	256.0	256.0	256.0	256.0	256.0	256.0	256.0
row_sparsity_mean_query	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375
row_non_zero_mean_corpus	256.0	256.0	256.0	256.0	256.0	256.0	256.0	256.0	256.0	256.0	256.0	256.0	256.0
row_sparsity_mean_corpus	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375	0.9375

Sparse Nano BEIR

• Dataset: NanoBEIR_mean
• Evaluated with SparseNanoBEIREvaluator with these parameters:

  {
      "dataset_names": [
          "climatefever",
          "dbpedia",
          "fever",
          "fiqa2018",
          "hotpotqa",
          "msmarco",
          "nfcorpus",
          "nq",
          "quoraretrieval",
          "scidocs",
          "arguana",
          "scifact",
          "touche2020"
      ]
  }
  

Metric	Value
dot_accuracy@1	0.547
dot_accuracy@3	0.7474
dot_accuracy@5	0.8014
dot_accuracy@10	0.8677
dot_precision@1	0.547
dot_precision@3	0.348
dot_precision@5	0.2697
dot_precision@10	0.1833
dot_recall@1	0.3319
dot_recall@3	0.5068
dot_recall@5	0.5645
dot_recall@10	0.6384
dot_ndcg@10	0.6006
dot_mrr@10	0.6584
dot_map@100	0.5229
row_non_zero_mean_query	256.0
row_sparsity_mean_query	0.9375
row_non_zero_mean_corpus	256.0
row_sparsity_mean_corpus	0.9375

Training Details

Training Dataset

natural-questions

• Dataset: natural-questions at f9e894e
• Size: 99,000 training samples
• Columns: query and answer
• Approximate statistics based on the first 1000 samples:

  	query	answer
  type	string	string
  details	min: 10 tokens mean: 11.71 tokens max: 26 tokens	min: 4 tokens mean: 131.81 tokens max: 450 tokens

• Samples:

  query	answer
  who played the father in papa don't preach	Alex McArthur Alex McArthur (born March 6, 1957) is an American actor.
  where was the location of the battle of hastings	Battle of Hastings The Battle of Hastings[a] was fought on 14 October 1066 between the Norman-French army of William, the Duke of Normandy, and an English army under the Anglo-Saxon King Harold Godwinson, beginning the Norman conquest of England. It took place approximately 7 miles (11 kilometres) northwest of Hastings, close to the present-day town of Battle, East Sussex, and was a decisive Norman victory.
  how many puppies can a dog give birth to	Canine reproduction The largest litter size to date was set by a Neapolitan Mastiff in Manea, Cambridgeshire, UK on November 29, 2004; the litter was 24 puppies.[22]

• Loss: CSRLoss with these parameters:

  {
      "beta": 0.1,
      "gamma": 1.0,
      "loss": "SparseMultipleNegativesRankingLoss(scale=1.0, similarity_fct='dot_score')"
  }
  

Evaluation Dataset

natural-questions

• Dataset: natural-questions at f9e894e
• Size: 1,000 evaluation samples
• Columns: query and answer
• Approximate statistics based on the first 1000 samples:

  	query	answer
  type	string	string
  details	min: 10 tokens mean: 11.69 tokens max: 23 tokens	min: 15 tokens mean: 134.01 tokens max: 512 tokens

• Samples:

  query	answer
  where is the tiber river located in italy	Tiber The Tiber (/ˈtaɪbər/, Latin: Tiberis,[1] Italian: Tevere [ˈteːvere])[2] is the third-longest river in Italy, rising in the Apennine Mountains in Emilia-Romagna and flowing 406 kilometres (252 mi) through Tuscany, Umbria and Lazio, where it is joined by the river Aniene, to the Tyrrhenian Sea, between Ostia and Fiumicino.[3] It drains a basin estimated at 17,375 square kilometres (6,709 sq mi). The river has achieved lasting fame as the main watercourse of the city of Rome, founded on its eastern banks.
  what kind of car does jay gatsby drive	Jay Gatsby At the Buchanan home, Jordan Baker, Nick, Jay, and the Buchanans decide to visit New York City. Tom borrows Gatsby's yellow Rolls Royce to drive up to the city. On the way to New York City, Tom makes a detour at a gas station in "the Valley of Ashes", a run-down part of Long Island. The owner, George Wilson, shares his concern that his wife, Myrtle, may be having an affair. This unnerves Tom, who has been having an affair with Myrtle, and he leaves in a hurry.
  who sings if i can dream about you	I Can Dream About You "I Can Dream About You" is a song performed by American singer Dan Hartman on the soundtrack album of the film Streets of Fire. Released in 1984 as a single from the soundtrack, and included on Hartman's album I Can Dream About You, it reached number 6 on the Billboard Hot 100.[1]

• Loss: CSRLoss with these parameters:

  {
      "beta": 0.1,
      "gamma": 1.0,
      "loss": "SparseMultipleNegativesRankingLoss(scale=1.0, similarity_fct='dot_score')"
  }
  

Training Hyperparameters

Non-Default Hyperparameters

• eval_strategy: steps
• per_device_train_batch_size: 64
• per_device_eval_batch_size: 64
• learning_rate: 4e-05
• num_train_epochs: 1
• bf16: True
• load_best_model_at_end: True
• batch_sampler: no_duplicates

All Hyperparameters

Click to expand

• overwrite_output_dir: False
• do_predict: False
• eval_strategy: steps
• prediction_loss_only: True
• per_device_train_batch_size: 64
• per_device_eval_batch_size: 64
• per_gpu_train_batch_size: None
• per_gpu_eval_batch_size: None
• gradient_accumulation_steps: 1
• eval_accumulation_steps: None
• torch_empty_cache_steps: None
• learning_rate: 4e-05
• weight_decay: 0.0
• adam_beta1: 0.9
• adam_beta2: 0.999
• adam_epsilon: 1e-08
• max_grad_norm: 1.0
• num_train_epochs: 1
• max_steps: -1
• lr_scheduler_type: linear
• lr_scheduler_kwargs: {}
• warmup_ratio: 0.0
• warmup_steps: 0
• log_level: passive
• log_level_replica: warning
• log_on_each_node: True
• logging_nan_inf_filter: True
• save_safetensors: True
• save_on_each_node: False
• save_only_model: False
• restore_callback_states_from_checkpoint: False
• no_cuda: False
• use_cpu: False
• use_mps_device: False
• seed: 42
• data_seed: None
• jit_mode_eval: False
• use_ipex: False
• bf16: True
• fp16: False
• fp16_opt_level: O1
• half_precision_backend: auto
• bf16_full_eval: False
• fp16_full_eval: False
• tf32: None
• local_rank: 0
• ddp_backend: None
• tpu_num_cores: None
• tpu_metrics_debug: False
• debug: []
• dataloader_drop_last: False
• dataloader_num_workers: 0
• dataloader_prefetch_factor: None
• past_index: -1
• disable_tqdm: False
• remove_unused_columns: True
• label_names: None
• load_best_model_at_end: True
• ignore_data_skip: False
• fsdp: []
• fsdp_min_num_params: 0
• fsdp_config: {'min_num_params': 0, 'xla': False, 'xla_fsdp_v2': False, 'xla_fsdp_grad_ckpt': False}
• fsdp_transformer_layer_cls_to_wrap: None
• accelerator_config: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None}
• deepspeed: None
• label_smoothing_factor: 0.0
• optim: adamw_torch
• optim_args: None
• adafactor: False
• group_by_length: False
• length_column_name: length
• ddp_find_unused_parameters: None
• ddp_bucket_cap_mb: None
• ddp_broadcast_buffers: False
• dataloader_pin_memory: True
• dataloader_persistent_workers: False
• skip_memory_metrics: True
• use_legacy_prediction_loop: False
• push_to_hub: False
• resume_from_checkpoint: None
• hub_model_id: None
• hub_strategy: every_save
• hub_private_repo: None
• hub_always_push: False
• gradient_checkpointing: False
• gradient_checkpointing_kwargs: None
• include_inputs_for_metrics: False
• include_for_metrics: []
• eval_do_concat_batches: True
• fp16_backend: auto
• push_to_hub_model_id: None
• push_to_hub_organization: None
• mp_parameters:
• auto_find_batch_size: False
• full_determinism: False
• torchdynamo: None
• ray_scope: last
• ddp_timeout: 1800
• torch_compile: False
• torch_compile_backend: None
• torch_compile_mode: None
• dispatch_batches: None
• split_batches: None
• include_tokens_per_second: False
• include_num_input_tokens_seen: False
• neftune_noise_alpha: None
• optim_target_modules: None
• batch_eval_metrics: False
• eval_on_start: False
• use_liger_kernel: False
• eval_use_gather_object: False
• average_tokens_across_devices: False
• prompts: None
• batch_sampler: no_duplicates
• multi_dataset_batch_sampler: proportional

Training Logs

Epoch	Step	Training Loss	Validation Loss	NanoMSMARCO_128_dot_ndcg@10	NanoNFCorpus_128_dot_ndcg@10	NanoNQ_128_dot_ndcg@10	NanoBEIR_mean_128_dot_ndcg@10	NanoMSMARCO_256_dot_ndcg@10	NanoNFCorpus_256_dot_ndcg@10	NanoNQ_256_dot_ndcg@10	NanoBEIR_mean_256_dot_ndcg@10	NanoClimateFEVER_dot_ndcg@10	NanoDBPedia_dot_ndcg@10	NanoFEVER_dot_ndcg@10	NanoFiQA2018_dot_ndcg@10	NanoHotpotQA_dot_ndcg@10	NanoMSMARCO_dot_ndcg@10	NanoNFCorpus_dot_ndcg@10	NanoNQ_dot_ndcg@10	NanoQuoraRetrieval_dot_ndcg@10	NanoSCIDOCS_dot_ndcg@10	NanoArguAna_dot_ndcg@10	NanoSciFact_dot_ndcg@10	NanoTouche2020_dot_ndcg@10	NanoBEIR_mean_dot_ndcg@10
-1	-1	-	-	0.5920	0.2869	0.6003	0.4930	0.5785	0.3370	0.6392	0.5183	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.0646	100	0.3598	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.1293	200	0.3648	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.1939	300	0.3272	0.3362	0.5728	0.2771	0.5552	0.4684	0.5932	0.3225	0.6162	0.5107	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.2586	400	0.3534	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.3232	500	0.3423	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.3878	600	0.3601	0.3204	0.5672	0.2679	0.5813	0.4721	0.611	0.3195	0.6453	0.5253	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.4525	700	0.3279	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.5171	800	0.3235	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.5818	900	0.3359	0.3098	0.5840	0.2496	0.5808	0.4715	0.6014	0.3208	0.6265	0.5162	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.6464	1000	0.3215	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.7111	1100	0.325	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.7757	1200	0.3394	0.3065	0.5838	0.2449	0.5739	0.4676	0.6022	0.3227	0.6069	0.5106	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.8403	1300	0.331	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.9050	1400	0.3188	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.9696	1500	0.3225	0.3034	0.5701	0.2706	0.5760	0.4722	0.6020	0.3186	0.6113	0.5107	-	-	-	-	-	-	-	-	-	-	-	-	-	-
-1	-1	-	-	-	-	-	-	-	-	-	-	0.3182	0.6035	0.8475	0.4422	0.8076	0.6106	0.3188	0.6459	0.9508	0.4004	0.6565	0.7238	0.4824	0.6006

• The bold row denotes the saved checkpoint.

Environmental Impact

Carbon emissions were measured using CodeCarbon.

• Energy Consumed: 0.136 kWh
• Carbon Emitted: 0.053 kg of CO2
• Hours Used: 0.398 hours

Training Hardware

• On Cloud: No
• GPU Model: 1 x NVIDIA GeForce RTX 3090
• CPU Model: 13th Gen Intel(R) Core(TM) i7-13700K
• RAM Size: 31.78 GB

Framework Versions

• Python: 3.11.6
• Sentence Transformers: 4.2.0.dev0
• Transformers: 4.49.0
• PyTorch: 2.6.0+cu124
• Accelerate: 1.5.1
• Datasets: 2.21.0
• Tokenizers: 0.21.1

Citation

BibTeX

Sentence Transformers

@inproceedings{reimers-2019-sentence-bert,
    title = "Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks",
    author = "Reimers, Nils and Gurevych, Iryna",
    booktitle = "Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing",
    month = "11",
    year = "2019",
    publisher = "Association for Computational Linguistics",
    url = "https://arxiv.org/abs/1908.10084",
}

CSRLoss

@misc{wen2025matryoshkarevisitingsparsecoding,
      title={Beyond Matryoshka: Revisiting Sparse Coding for Adaptive Representation},
      author={Tiansheng Wen and Yifei Wang and Zequn Zeng and Zhong Peng and Yudi Su and Xinyang Liu and Bo Chen and Hongwei Liu and Stefanie Jegelka and Chenyu You},
      year={2025},
      eprint={2503.01776},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2503.01776},
}

SparseMultipleNegativesRankingLoss

@misc{henderson2017efficient,
    title={Efficient Natural Language Response Suggestion for Smart Reply},
    author={Matthew Henderson and Rami Al-Rfou and Brian Strope and Yun-hsuan Sung and Laszlo Lukacs and Ruiqi Guo and Sanjiv Kumar and Balint Miklos and Ray Kurzweil},
    year={2017},
    eprint={1705.00652},
    archivePrefix={arXiv},
    primaryClass={cs.CL}
}